Dear respected,
Good day! Thanks for posting in our community.
We are sorry to hear that you're experiencing issues with inserting online pictures in Microsoft Office 2016 application on your Windows 11 laptop. In this situation, as moderators in this category mainly focus on Microsoft 365 for Business subscription, we have limited support resources and test environment for Office 2016 product. We suggest you may get the professional support from the dedicated support community: Home - Microsoft Community Hub.
And from my search, here is a similar thread for reference. It seems like some other users are having the same issue with you.
Bad Request - HTTP Error 400. The size of the request headers is too long. Error inserting Photos - Microsoft Community Hub
Feel free to come back with us if there have anything else I can do for you and we will offer the further support as much as we can. Appreciate your patience and understanding and thanks for your time and cooperation. Hope you a nice day!
Sincerely,
Mia | Microsoft Community Moderator